2.7
Théorème de superposition
Le principe de superposition est un concept fondamental selon lequel dans un circuit linéaire, la tension aux bornes (ou le courant traversant) un élé…
Le théorème de superposition est utilisé dans les circuits avec plusieurs sources indépendantes.
Pour appliquer ce théorème, il faut conserver une source indépendante à la fois tout en remplaçant la source de tension inactive par un court-circuit et la source de courant inactive par un circuit ouvert, respectivement.
Le théorème stipule que la tension ou le courant traversant un élément dans un circuit linéaire est la somme algébrique des contributions des sources indépendantes.
Considérons un circuit avec une tension et une source de courant, où la chute de tension aux bornes d’une résistance doit être déterminée.
La chute de tension a des contributions des deux sources indépendantes.
La contribution de la source de tension est obtenue en mettant la source de courant à zéro.
En appliquant la loi de tension de Kirchhoff, le courant de boucle est déterminé. À l'aide de la loi d'Ohm, la chute de tension est calculée.
De même, la contribution de la source de courant est obtenue en mettant la source de tension à zéro.
En combinant les résistances, on obtient une résistance équivalente. À l'aide de la règle de division du courant et de la loi d'Ohm, la chute de tension est déterminée.
Enfin, en additionnant les contributions de sources indépendantes, on obtient la chute de tension totale aux bornes de la résistance.
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Q1: What is the superposition theorem and when should you use it?
The superposition theorem applies to linear circuits with multiple independent sources. It states that voltage across or current through any element equals the algebraic sum of contributions from each independent source acting alone. Deactivate all sources except one, analyze the circuit, then repeat for each source. Finally, add all contributions together to find the total response.
Q2: How do you deactivate sources when applying superposition?
Replace inactive voltage sources with short circuits and inactive current sources with open circuits. This deactivation process isolates each independent source's contribution. Keep only one source active while deactivating all others, then analyze the simplified circuit using standard techniques like Ohm's law and Kirchhoff's voltage law.
Q3: Why does superposition work differently for dependent and independent sources?
Dependent sources remain active during superposition analysis because they are governed by circuit variables, not external inputs. Only independent sources are deactivated one at a time. This distinction ensures dependent sources continue responding to the circuit conditions created by the active independent source being analyzed.
Q4: What steps do you follow to find voltage drop across a resistor using superposition?
First, set the current source to zero and calculate the voltage drop contribution from the voltage source using Kirchhoff's voltage law and Ohm's law. Next, set the voltage source to zero, find equivalent resistance, apply current division, and calculate the voltage drop from the current source. Finally, add both contributions algebraically to obtain the total voltage drop.
Q5: What is a drawback of using the superposition theorem for circuit analysis?
Superposition requires analyzing multiple simplified circuits, one for each independent source. A circuit with three independent sources demands three separate analyses, increasing computational effort compared to single-pass methods. Despite this added work, superposition remains valuable for simplifying complex multi-source circuits and verifying solutions.
Q6: How does superposition relate to other circuit analysis methods?
Superposition complements analysis techniques like nodal analysis and mesh analysis by breaking complex circuits into simpler components. While nodal analysis and mesh analysis solve circuits directly, superposition isolates each source's effect separately. Both approaches work on linear circuits but offer different computational pathways depending on circuit topology and source configuration.
Q7: Can you apply superposition to circuits with both voltage and current sources?
Yes, superposition applies to circuits containing both voltage and current sources since both are independent sources. Analyze the circuit with only the voltage source active by replacing the current source with an open circuit, then analyze with only the current source active by replacing the voltage source with a short circuit. Sum the individual contributions to find the total response.